Revisiting the phase structure of the Polyakov-quark-meson model in the presence of vacuum fermion fluctuation

We have considered the contribution of fermionic vacuum loop in the effective potential of Polyakov loop extended quark-meson model (PQM) for the two-quark flavor case and explored the phase structure and thermodynamics of the resulting PQMVT model (Polyakov-quark-meson model with vacuum term) in detail at nonzero as well as zero chemical potential. The temperature variations of order parameters and their derivatives have been calculated and the phase diagram together with the location of critical end point (CEP) has been obtained in $\ensuremath{\mu}$, and $T$ plane in both the models PQMVT and PQM. The PQMVT model analysis has been compared with the calculations in PQM model in order to bring out the effect of fermionic vacuum term on the physical observables. The sensitivity of the phase structure and location of the CEP to the choice of Polyakov loop potential and sigma meson mass value has also been explored in the PQMVT model. We notice that the CEP which is located near the temperature axis at ($\ensuremath{\mu}=81\text{ }\text{ }\mathrm{MeV}$, $T=167\text{ }\text{ }\mathrm{MeV}$) in the PQM model gets shifted close to the chemical potential axis at (${\ensuremath{\mu}}_{\mathrm{CEP}}=294.7$, ${T}_{\mathrm{CEP}}=84.0\text{ }\text{ }\mathrm{MeV}$) in the PQMVT model calculations of the phase diagram. Since it emerges from a background of second-order transition in the chiral limit of massless quarks, the crossover occurring at $\ensuremath{\mu}=0$ in PQMVT model for the realistic case of explicitly broken chiral symmetry, has been identified as quite a soft and smooth transition. We have presented and compared the results for temperature variations of thermodynamic observables at zero and different nonzero quark chemical potentials. It is noticed that the presence of fermionic vacuum term in the effective potential leads to a smoother and slower temperature variation of thermodynamic quantities.